Cordova, which uses HTML in a WebView paradigm, lets you wrap native API's as plugins, so you can access them from JavaScript. You can access most (all?) native functionality from within JS using either Corfova-supplied or third party plugins. Honestly, Cordova + Ionic/Angular has been a great experience so far. Very few problems and a super quick time to market. I can't imagine iterating as quickly for two platforms at once (three if you care about Windows Mobile).
Yes, but you don't get a native UI with hybrid solutions like Cordova. Also, in order to use native APIs, you have to create special wrappers for them, whereas in NativeScript, it looks like you can call the APIs directly. (How this affects performance, I don't know.)
How does calling API's directly work with different platforms using different names, calling conventions, etc.? I like that with Cordova someone already did the work of normalizing the native calls.
Agreed about the lack of native UI. Things like Ionic help, but it is not 100% perfect by any means.